Problem 3
Finding the Area between Two Polar Curves Find the area outside the cardioid \(r=2+2 \sin \theta\) and inside the circle \(r=6 \sin \theta\).
Problem 3
Sketch the curves below by eliminating the parameter \(t\). Give the orientation of the curve. $$ x=2 t+4, y=t-1 $$
Problem 3
Plot each of the following points on the polar plane. a. \(\left(2, \frac{\pi}{4}\right)\) b. \(\left(-3, \frac{2 \pi}{3}\right)\) c. \(\left(4, \frac{5 \pi}{4}\right)\)
Problem 4
Sketch the curves below by eliminating the parameter \(t\). Give the orientation of the curve. $$ x=3-t, y=2 t-3,1.5 \leq t \leq 3 $$
Problem 4
Put the equation \(2 y^{2}-x+12 y+16=0\) into standard form and graph the resulting parabola.
Problem 4
Plot \(\left(4, \frac{5 \pi}{3}\right)\) and \(\left(-3,-\frac{7 \pi}{2}\right)\) on the polar plane.
Problem 5
Finding a Second Derivative Calculate the second derivative \(d^{2} y / d x^{2}\) for the plane curve defined by the parametric equations \(x(t)=t^{2}-3, y(t)=2 t-1,-3 \leq t \leq 4\)
Problem 5
Graph the curve defined by the function \(r=4 \sin \theta\). Identify the curve and rewrite the equation in rectangular coordinates.
Problem 5
Finding the Arc Length of a Polar Curve Find the arc length of the cardioid \(r=2+2 \cos \theta\).
Problem 5
Eliminate the parameter and sketch the graphs. $$ x=2 t^{2}, \quad y=t^{4}+1 $$
